This thesis presents a mathematical framework for precision attitude control of a spacecraft using the inertial coupling between the spacecraft and solar arrays. The spacecraft with solar arrays is modeled as a one degree of freedom cylinder (rigid body rotation) with flexible appendages (infinite-dimensional system). The equations of motion that describe system evolution are derived using the extend generalizations of the Lagrangian for infinite dimension systems. Precision attitude control is achieved by bending the flexible appendage using strain actuators. Global asymptotic convergence of the controller’s is proved using the Lyapunov direct method, which ensures that the control objectives of trajectory tracking and slewing are achieved. The Input-to-State stability of these controllers is used to generalize the control laws in terms of a variable that scales the stiffness term. The closed-loop system is simulated numerically for different values of the variable to verify stability.
An experimental setup, that mimics a spacecraft with solar arrays is designed as a cylinder that is secured to a flexible beam using an interference fit. The strain actuation of the beam is achieved using piezoelectric actuators. The rotation of the cylinder and bending in beam are estimated using measurements from a Vicon motion capture system. The closed-loop system is tested in real-time to achieve controlled rotation of the cylinder.